What’s the answer for this problem

Answer:

The following linear equation represents the system:

x + y = 20 (speed of the riverboat and current in km/hr in the same direction)

x - y = 16 (speed of the riverboat relative to the current in km/hr in opposite directions)

Solving for x and y gives us:

x = 18 and y = 2 (speed of the riverboat and current in km/hr).

Step-by-step explanation:

The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).

What is vector ?

A vector is a mathematical object that has both magnitude (or length) and direction. Vectors can be used to represent physical quantities such as velocity, force, or displacement, where the magnitude represents the size of the quantity and the direction represents its orientation in space.

Let n1 and n2 be the normal vectors of the two planes, respectively.

The normal vectors are:

n1 = <5, -4, -1> and n2 = <5, -4, 1>.

The projection of n1 onto n2 is:

projn1 onto n2 = (n1 . n2 / ||n2||^2) * n2 = (n1 . n2 / ||n2||^2) * (n2 / ||n2||) = (n1 . n2 / ||n2||) * n2 / ||n2|| = (n1 . n2) * n2 / ||n2||^2.

The dot product of n1 and n2 is:

n1 . n2 = 5 * 5 + (-4) * (-4) + (-1) * 1 = 25 + 16 + 1 = 42.

The magnitude of n2 is:

||n2|| = sqrt(5^2 + (-4)^2 + 1^2) = sqrt(30).

Therefore, the projection of n1 onto n2 is:

(n1 . n2) * n2 / ||n2||^2 = 42 * <5, -4, 1> / 30 = <7/3, -4/3, 7/30>.

So , The distance between the two planes 5x−4y−z=65x−4y−z=6 and 4y−5x z=−484y−5x z=−48 is sqrt(7/10).

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The mode frequency can be a useful tool for understanding the distribution of the data and identifying any outliers or anomalies in the data set.

The mode frequency of the age variable refers to the most frequently occurring age in a given set of data. This measure of central tendency is particularly useful when working with categorical data, such as age ranges.

To calculate the mode frequency, one must first organize the data into a frequency distribution table, which lists all the different ages and the number of times each occurs. The age with the highest frequency is then considered the mode frequency.

For example, if there are 100 individuals in a data set and the ages range from 20 to 60, we would organize the data into age ranges, such as 20-29, 30-39, etc. Then we would count how many individuals fall into each age range and record this information in the frequency distribution table.

If the age range with the highest frequency occurs more than once, we have a multi-modal data set. On the other hand, if there is only one mode frequency, the data set is considered unimodal.

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The system of equation (4) and (5) have no solution

From the question, we have the following parameters that can be used in our computation:

7(5x + 2) = 5x + 2

Divide both sides by 5x + 2

7 = 1

This equation is false, meaning there is no solution for y that satisfies both equations.

Here, we have

2y = 6

y = -15

Since these are two different equations with the same variable, y, we can use substitution to find a solution.

Starting with the second equation, y = -15, we can substitute this value into the first equation:

2y = 6

2(-15) = 6

-30 = 6

This equation is false, meaning there is no solution for y that satisfies both equations.

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Complete question

4. How many solutions will this equation have? 7(5x + 2) = 5x + 2

5. Solve the given system of equations 2y = 6 and y = -15

The tangent of the angle between vectors v and w is 2√(21) / 9

We can use the dot product and cross-product formulas to find the angle between two vectors.

The dot product of two vectors v and w is given by:

v · w = ||v|| ||w|| cos(θ)

where ||v|| and ||w|| are the magnitudes of the vectors v and w, and θ is the angle between them.

The cross product of two vectors v and w is given by:

v × w = ||v|| ||w|| sin(θ) k

where k is a unit vector in the direction of the cross product.

Since v × w = 6i - 7j + 9k and v · w = 9, we can find the angle between v and w as follows:

[tex]\theta = sin^{-1}\frac{||v \times w||}{||v|| \ ||w||} = sin^{-1}\frac{||6i - 7j + 9k||}{||v|| \ ||w||}[/tex]

We can find the magnitude of v × w by using the formula for the magnitude of a cross-product:

[tex]||v \times w|| = ||6i - 7j + 9k|| \\\\= \sqrt{6^2 + (-7)^2 + 9^2} = \sqrt{6^2 + 49 + 9^2}\\\\=\sqrt{84} = \sqrt(2^2 \times 3 \times 7) = 2\sqrt{(3 \times 7)[/tex]

We can find the magnitude of v and w using the given dot product formula:

v · w = ||v|| ||w|| cos(θ) = 9

||v|| ||w|| = 9 / cos(θ)

Since we know that ||v|| and ||w|| are positive, we can square both sides to obtain:

[tex](||v|| \ ||w||)^2 = \frac{9 }{cos(\theta))^2} \\\\||v||^2 \ ||w||^2 = \frac{81}{cos^2(\theta)}[/tex]

Finally, using the tangent formula, we can find tanθ:

tan(θ) = sin(θ) / cos(θ) = ||v × w|| / ||v·w|| = 2√(3 × 7) / 9 = 2√(21) / 9.

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The expected Net gain is -0.1001.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total possible selection = 10000

                  Net Gain             Probability

Win                8998                   1/ 10000

Lose                 2                     9999/10000

So, E(x) = 8998 x 1/10000 - 9999/10000

             = -1001 / 10000

so, the expected Net gain = -0.1001

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Answer:

he ran 280 miles more than Michael

Step-by-step explanation:

438-158=280

Answer:

m= -3/2

Step-by-step explanation:

To find slope

[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]

We have our x1 and y1 of (2,5)

We have our x2 and y2 of (8,-4)

Now we plug in

= (-4-5)/(8-2)

= (-9)/(6)

Simplifying it would be

[tex]m = - \frac{3}{2} [/tex]

Answer: slope 'm' = -3 / 2

Step-by-step explanation: Using the formula m=(y2-y1)/(x2-x1), where 'm' is the slope of the line connecting the two points, we can plug in our x and y values:

x1 = 2

x2 = 8

y1 = 5

y2 = -4

Once we plug in our x and y values, we get the equation

m = (-4 - 5) / (8 - 2)

--> -9 / 6 (We can simplify this fraction to get or answer of -3 / 2)

The coins of each type are 346 nickels, 165 dimes and 173 quarters. when a newspaper carrier has $6.85 charge  by substitution method.

Let x = number of quarters

Then, x-4 = number of dimes and 5x = number of nickels

So, 0.05(5x) + 0.10(x-4) + 0.25x = 6.85

0.6x - 0.4 = 6.85

0.6x = 7.25

x = 12

There are 12 quarters, 8 dimes, and 60 nickels (or)

x = 8 + D(dimes)

D = Q -8

N(nickels) = 2Q

N + D + Q = 685

2Q + Q-8 + Q = 685

4Q = 685+ 8 = 693

Q = 693/4 = over 173

D= over 165

N= over 346

174+ 165 + 346 = 685

the answer is 346 nickels, 165 dimes and 174 quarters.

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Answer: 3/4

Step-by-step explanation:

15/32 + 9/32 = 24/32 = 12/16 = 6/8 = 3/4

The monthly loan payment for the offer made by Juanita, given the cost of the car and the dealership, is A. 248.62

First, find the amount taken on loan :

= 15, 000 x ( 1 - 10 % down payment )

= $ 13, 500

The periodic rate is:

= 4 % / 12

= 1 / 3 %

The number of periods :

= 5 years x 12 months a year

= 60 months

The monthly payment is:

Present value of loan = Monthly Payment x Present value interest factor of annuity, 1 / 3 %, 60 months

13, 500 = 54.299068906557 x Monthly payment

Monthly payment = 13, 500 / 54.299068906557

= 248. 62

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The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes, 7.444

Standard deviation is a measure of the spread or dispersion of a set of data. It quantifies how much the individual data points in a set deviate from the mean (average) value of the set. In other words, it tells you how much the data is scattered around the mean.

The test statistic to test the claim that the standard deviation of all customer waiting times is greater than 3.5 minutes can be calculated using the following formula:

Z = (s / σ) x √n

where s is the sample standard deviation (4.8 minutes), σ is the population standard deviation (3.5 minutes), and n is the sample size (15).

Z = (4.8 / 3.5) x √15

  = 7.444

So the test statistic is 7.444.

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It is an inferential technique that uses the data from a sample to draw inferences about a population.

Hypothesis testing is a type of statistical hypothesis that uses data from a sample to draw judgments about a population parameter or a population probability distribution.

First, an uncertain hypothesis is made about the parameter or distribution. This is named the null hypothesis and is denoted by [tex]H_{O}[/tex]. An alternative hypothesis (denoted [tex]H_{a}[/tex]), which is the opposite of the null hypothesis, is then described.

The hypothesis-testing process involves using sample data to decide whether or not [tex]H_{0}[/tex] can be rejected. If [tex]H_{O}[/tex] is rejected, the statistical determination is that the alternative hypothesis [tex]H_{a[/tex] is true.

Hence, the correct answer is c.

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--The given question is incorrect; the correct question is

"A hypothesis test is

a. a descriptive technique that allows researchers to describe a sample

b. a descriptive technique that allows researchers to describe a population

c. an inferential technique that uses the data from a sample to draw inferences about a population

d. an inferential technique that uses information about the population to make predictions about a sample"--

An equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y),  400 + 70x

The number of customers served after 12 months, 1240

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

In the first month, the coffee shop served 400 customers

After that, the coffee shop served 70 customers each month

Suppose, coffee shop served x number of months after first month,

Total people served = 400 + 70x

The number of customers served after 12 months,

Total people served = 400 + 70x12

                                  = 400 + 840

                                  = 1240

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Answer:

No solution

Step-by-step explanation:

1/3x-y=2  

x - 3y = 6​

Times the first equation by -3

-x + 3y = -6

x - 3y = 6

0 = 0

So, there is no solution.

Answer:

21[tex]e^{6}[/tex] and 30[tex]t^{6}[/tex][tex]v^{10}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

given

3e³ × 7e³

= 3 × 7 × e³ × e³

= 21 × [tex]e^{(3+3)}[/tex]

= 21[tex]e^{6}[/tex]

-------------------------------

(10[tex]t^{4}[/tex][tex]v^{5}[/tex] )(3t²[tex]v^{5}[/tex] )

= 10 × 3 × [tex]t^{4}[/tex] × t² × [tex]v^{5}[/tex] × [tex]v^{5}[/tex]

= 30 × [tex]t^{(4+2)}[/tex] × [tex]v^{(5+5)}[/tex]

= 30[tex]t^{6}[/tex][tex]v^{10}[/tex]

Answer:

6(x-0)=-8

6x=-8

6x/6=-8/6

Hope this helps!!

Step-by-step explanation:

Answer: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Let the number be x

6 times x = 6x

subtracted from 0

gives -8

∴ 0 - 6x = -8

0 + 8 = 6x

[tex]\frac{8}{6}[/tex] = x

[tex]\frac{4}{3}[/tex] = x

Investment in automation cost = $8,750,000 when there

no further change in capacity.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Following are the informations of Cent:

Current automation = 7%

Capacity of next round = 1,100

New automation = 7 + 2 = 9

Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000

= 1,100 * (4 * (9 - 7)) * 1,000

= 1,100 * (4 * 2) * 1000

= 1,100 * 8 * 1,000

= $8,800,000.

Investment in automation cost = $8,800,000.

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Answer is Taking data:

                        28 78 74 89 72

                        50 55 66 26 84

                        59 64 88 23 27

                        70 63 42 37 29

The answer is width of class =13

As the data is not given in the question I'm guessing the data from the question I solved before

28 78 74 89 72

50 55 66 26 84

59 64 88 23 27

70 63 42 37 29

as taking the above data,

maximum value=89

minimum value=23

no : of classes scores are divided into=5 classes

As we know for finding the width of class:

width of class = (maximum value-minimum value)/ no ; of classes

width = (89-23)/5=66/5

width=13.2=13

Note : By using the above given formula you can calculate the width of any data just by taking the maximum and minimum values of data and the number of classes the data is divided into.

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The x-intercept of the function as an ordered pair is equal to (5, 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value with zero (0) by substituting it into the given equation y = ∛x - 5 as follows;

y = ∛x - 5

0 = ∛x - 5

Taking the cube root of both sides of the function, we have the following:

0 = x - 5

x = 5

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When it is third and long, the best move is typically to make a long pass to a wide receiver because it has the probability to gain the greatest yardage.

Throwing the ball far downfield is frequently the best move when the team has to gain a lot of yardage to continue the drive on third and long. The most yards may be gained by a deep pass to a wide receiver since it might extend the action past the original line of scrimmage. The prospect of a huge play, in which the receiver catches the ball and runs for a bigger gain, is also made possible. A deep pass might also throw the defense off because they might not be anticipating the offense to go for a long gain. But a deep pass can also be dangerous because it might result in a turnover if the receiver doesn't pay attention.

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The surface area of an egg shell scales as the mass of the egg shell raised to 1.82694

The term surface area in math is defined as the area occupied by a three-dimensional object by its outer surface

Here we know that the area of a cube with edged is proportional to the second power d² while its volume is proportional to the third power d³.

Here we know that for any bounded solid object, here we have which encloses a region with some volume V and its enclosing surface has area A, where as the same kind of proportions can be derived in terms of a linear dimension d of the object, here for example the diameter of the object.

AS we all know that the surface area is directly proportional to the 3rd power of the mass of the egg, here we have A = km³ where A is the surface area, k a constant of proportionality, and m the mass.

For a chicken egg we have 28 = k(60)⁰°⁶⁷

Here by solving for k we get:

=> k = 28/60⁰°⁶⁷ ≈ 1.82694

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the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ]  is the formula in terms of i and n for the gernal left endpoint x i-1

What is the formula for left endpoint approximation?

Rule: Left-Endpoint Approximation

On each subinterval [xi−1,xi] (for i=1,2,3,…,n), construct a rectangle with width Δx and height equal to f(xi−1), which is the function value at the left endpoint of the subinterval. Then the area of this rectangle is f(xi−1)Δx

In this problem you will calculate ∫302+4 by using the formal definition of the definite integral: ∫()=lim→∞[∑=1(∗)Δ].

(a) The interval [0,3] is divided into equal subintervals of length Δ. What is Δ (in terms of )? Δ

(b) The right-hand endpoint of the th subinterval is denoted ∗. What is ∗ (in terms of and )

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Answer:It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.

give me a thanks and a 5 star pls!

Step-by-step explanation:

It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.

The closed form for the matrix l−1 is the inverse matrix of l, which corresponds to an elementary transformation of type 1, which is a row transformation.

A closed form for the matrix L-1 is given by the following formula:

L-1 = (1/det(L)) * adj(L)

Where "det(L)" represents the determinant of the matrix L, and "adj(L)" is the adjugate matrix of L. The adjugate matrix of a matrix A is the transpose of its cofactor matrix, and is denoted as adj(A). The cofactor matrix of a matrix is the matrix of determinants of the minors of the matrix multiplied by alternating signs.

The elementary transformation of type 1 is row interchange. This means that two rows of the matrix are interchanged with each other. This transformation has the same effect when applied from the left as from the right, so when multiplying with L-1 from the left, it corresponds to a row interchange.

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The equation 1.[tex]5^x[/tex] - x - 2 = 0 then the value of x be -1.44292524676275.

A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

Let the equation [tex]$1.5^x-x-2=0$[/tex]

Lambert form: [tex]$1=-e^{-\ln (1.5) x}(-x-2)$[/tex]

The equation with [tex]$(-x-2) \ln (1.5)=u$[/tex] and [tex]$x=-\frac{u+2 \ln (1.5)}{\ln (1.5)}$[/tex][tex]$1=-e^{-\ln (1.5)\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)}\left(-\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)-2\right)$$[/tex]

Simplifying the above equation, we get

[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$$[/tex]

[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$[/tex] in Lambert form: [tex]$e^u u=-\frac{\ln (1.5)}{2.25}$[/tex]

Solve [tex]$e^u u=-\frac{\ln (1.5)}{2.25}: \quad u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$[/tex]

[tex]$$u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$$[/tex]

Substitute back [tex]$u=(-x-2) \ln (1.5)$[/tex], solve for x[tex]$(-x-2) \ln (1.5)=W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right): \quad x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]

Therefore, the simplifying x, we get

[tex]$x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}, x=-\frac{W_0\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]

Therefore, the value of x be x = -1.44292524676275.

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Step-by-step explanation:

the slope is always the ratio of

y coordinate difference / x circumstances difference

when going from one point on the line to another.

1.

x changes by +3 (from 2 to 5).

y changes by -6 (from -1 to -7).

the slope is -6/+3 = -2.

m = -2, b = 3 is the correct answer

2.

x changes by +2 (from -4 to -2).

y changes by +3 (from -2 to 1).

the slope is +3/+2 = 3/2.

m = 3/2, b = 4 is the correct answer.

FYI

because there is in both cases only one answer option with the correct slope, we did not need to check the y-intercept ...

The value of square feet means 1 acre be 43,560 square feet.

The US measurement system uses the acre as the unit of land area measurement. Every real estate transaction and listing worldwide has a connection to Square Feet.

The length and width of the land—which are often stated in feet—are multiplied to determine the acreage before converting the result to square feet. Following that, the square footage is converted to acres using a conversion ratio of 43560.

For standing or stored water, an acre-foot is the accepted unit of measurement. It is the volume of water necessary to cover an acre of ground that is 43,560 square feet in size and one foot deep. 325,851 gallons make up an acre-foot.

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Answer:

The answer to the inequality is [tex]p\geq 4[/tex].

Step-by-step explanation:

Lets solve the inequality.

[tex]-2p\leq -8[/tex]

Divide both sides of the equation by -2.

There is an inequality rule that says when multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

First lets divide both sides by -2.

[tex]\frac{-2p}{2} \leq \frac{-8}{2}[/tex]

Simplify the left side by cancelling the common factor of −2.

[tex]p\leq \frac{-8}{2}[/tex]

Simplify the right side by dividing -8 by 2.

[tex]p\leq 4[/tex]

We need to flip the direction of the inequality sign.

[tex]p\geq 4[/tex]